Published, in part, as 8.97-99. Unpublished (pp. 3-8). Denial of either the first or second of the two "natural propositions," noted in that part of manuscript which was published, leads to a non-Euclidean geometry. Both of the corresponding kinds of non-Euclidean geometry are intelligible, and a consideration of plane geometry will suffice to show this.
Geometry, Euclidean (nonEuclidean), Mathematics